scholarly journals Micropolar fluid between two coaxial cylinders (numerical approach)

2021 ◽  
pp. 12-12
Author(s):  
Dusko Salemovic ◽  
Aleksandar Dedic ◽  
Bosko Jovanovic
Keyword(s):  
Mathematical Model ◽  
Symmetry Axis ◽  
Numerical Approach ◽  
Variable Coefficients ◽  
Constant Angular Velocity ◽  
Coaxial Cylinders ◽  
Complex Mathematical Model ◽  
Two Phases ◽  
Physical Analogy ◽  
The Continuum

The paper describes the flow of a suspension which is a mixture of two phases: liquid and solid granules. The continuum model with microstructure is introduced, which involves two independent kinematic quantities: the velocity vector and the micro-rotation vector. The physical analogy is based on the movement of the suspension between two coaxial cylinders. The inner cylinder is stationary and the outer one rotates with constant angular velocity. This physical analogy enabled a mathematical model in a form of two coupled differential equations with variable coefficients. The aim of the paper is to present the numerical aspect of the solution for this complex mathematical model. It is assumed that the solid granules are identically oriented and that under the influence of the fluid they move translationally or rotate around the symmetry axis but the direction of their symmetry axes does not change. The solution was obtained by the ordinary finite difference method, and then the corresponding sets of points (nodes) were routed by interpolation graphics.

To the question of creating a complex mathematical model of a production system

2020 ◽  
Keyword(s):  
Mathematical Model ◽  
Hierarchical Structure ◽  
Production System ◽  
Quality Criterion ◽  
Controlling Parameter ◽  
Complex Mathematical Model

One of the approaches to the development of a complex mathematical model of a production system is considered. Keywords mathematical model; target subsystem; quality criterion; controlling parameter; hierarchical structure

Mathematical modeling of Couette flow in anomalous thermoviscous liquid

2011 ◽  
Vol 8 (1) ◽  
pp. 143-152
Author(s):  
S.F. Khizbullina
Keyword(s):  
Mathematical Modeling ◽  
Angular Velocity ◽  
Numerical Experiment ◽  
Temperature Dependence ◽  
Steady Flow ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Flow Regimes ◽  
Constant Angular Velocity ◽  
Coaxial Cylinders

The steady flow of anomalous thermoviscous liquid between the coaxial cylinders is considered. The inner cylinder rotates at a constant angular velocity while the outer cylinder is at rest. On the basis of numerical experiment various flow regimes depending on the parameter of viscosity temperature dependence are found.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

scholarly journals Taking into account multi-axiality of loads on marine structures in their fatigue strength calculations

2019 ◽  
pp. 153-161
Author(s):  
Gennadiy Kryzhevich ◽  
Anatoliy Filatov
Keyword(s):  
Mathematical Model ◽  
Fatigue Strength ◽  
Axial Loading ◽  
Failure Criteria ◽  
Design Parameters ◽  
Optimal Assignment ◽  
Marine Structures ◽  
Fatigue Wear ◽  
Mathematical Simulations ◽  
Complex Mathematical Model

This paper studies marine structures made of steels and light alloys and exposed to cyclic operational loads. Stress-strain parameters of their joints were taken from mathematical simulations of loads and strains or from actual strain gauging data. The aim of this study is to develop recommendations on fatigue strength calculations: specifically, how to quite the complex mathematical model of multi-axial loading at critical structural points with fast fatigue wear in favour of a simplified stressstrain state description based on optimal assignment of design parameters (stresses) in fatigue failure criteria. Preferability of this approach depends on case-specific requirements to calculation accuracy and timeframes. Uniaxial description of stressed state instead of the three-axial one enables much faster calculation with acceptable drop in accuracy.

scholarly journals Mathematical modeling and algorithm for calculation of thermocatalytic process of producing nanomaterial

2021 ◽  
Vol 23 (3) ◽  
pp. 1590
Author(s):  
Bakhtiyar Ismailov ◽  
Zhanat Umarova ◽  
Khairulla Ismailov ◽  
Aibarsha Dosmakanbetova ◽  
Saule Meldebekova
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Solid Phase ◽  
Nonlinear Effects ◽  
Operating Characteristics ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Wide Range ◽  
The Laplace Transform ◽  
Complex Mathematical Model

<p>At present, when constructing a mathematical description of the pyrolysis reactor, partial differential equations for the components of the gas phase and the catalyst phase are used. In the well-known works on modeling pyrolysis, the obtained models are applicable only for a narrow range of changes in the process parameters, the geometric dimensions are considered constant. The article poses the task of creating a complex mathematical model with additional terms, taking into account nonlinear effects, where the geometric dimensions of the apparatus and operating characteristics vary over a wide range. An analytical method has been developed for the implementation of a mathematical model of catalytic pyrolysis of methane for the production of nanomaterials in a continuous mode. The differential equation for gaseous components with initial and boundary conditions of the third type is reduced to a dimensionless form with a small value of the peclet criterion with a form factor. It is shown that the laplace transform method is mainly suitable for this case, which is applicable both for differential equations for solid-phase components and calculation in a periodic mode. The adequacy of the model results with the known experimental data is checked.</p>

Active thrust fluid-film bearings: Theoretical and experimental studies

2019 ◽  
Vol 234 (2) ◽  
pp. 261-273 ◽  
Author(s):  
Alexander Babin ◽  
Alexey Kornaev ◽  
Alexey Rodichev ◽  
Leonid Savin
Keyword(s):  
Mathematical Model ◽  
Position Control ◽  
Experimental Studies ◽  
Axial Loading ◽  
Life Time ◽  
Fluid Film ◽  
Thrust Bearings ◽  
Active Fluid ◽  
Rotor Bearing ◽  
Complex Mathematical Model

Research in the field of active fluid-film bearing has been recently getting more and more attention, integration of control systems becoming one of the most promising means of enhancement of rotor-bearing nodes' characteristics. It has been determined that the vast majority of papers published on active fluid-film bearing only consider radial bearings, and very few focus on thrust bearings. This lack of attention along with the obvious necessity to fill the said gap has triggered the present research. In cases of rotor machines that experience extensive axial loading due to various reasons, e.g. various turbine engines (aero and spacecraft) and hydraulic pumps (crude oil extraction facilities), such research could prove the feasibility of application of a control system to significantly increase the performance of the whole machine. Moreover, extensive wear during start up and shut down could be eliminated by means of rotor position control, thus life time of a rotor-bearing system could be significantly increased. The present paper features a complex mathematical model of an active thrust fluid-film bearing with a central feeding orifice, a developed test rig designed to verify the presented mathematical model allowing a series of numerical tests to be carried out. Numerical studies focus on the hypothesis of a possibility to use active control in thrust bearings to decrease power loss due to friction and extensive axial vibrations by means of identification of an energy efficient area of axial gaps based on the lubrication regime and its maintenance by means of application of controlled lubrication principles.

scholarly journals Development of Complex Mathematical Model of Light Naphtha Isomerization and Rectification Processes

2014 ◽  
Vol 10 ◽  
pp. 236-243 ◽  
Author(s):  
Viacheslav A. Chuzlov ◽  
Nikita V. Chekantsev ◽  
Emilia D. Ivanchina
Keyword(s):  
Mathematical Model ◽  
Light Naphtha ◽  
Complex Mathematical Model

Residual Stress of Gear Meshing under Shakedown Condition with Direct Analysis

2012 ◽  
Vol 152-154 ◽  
pp. 877-882
Author(s):  
Yuan Yuan ◽  
Peng Fei Li ◽  
Kai Liu
Keyword(s):  
Mathematical Model ◽  
Residual Stress ◽  
Residual Stresses ◽  
Direct Method ◽  
Direct Analysis ◽  
Numerical Approach ◽  
Operating Life ◽  
Operator Split ◽  
Gear Contact ◽  
Residual Stresses And Strains

A shakedown mathematical model of gear contact has been developed. A direct method is applied to solve the mathematical model. Local coordinates are constructed on different meshing points because curvature of gear profile is not constant. Distributions of residual stresses and strains are given base on variable curvature surface. The numerical approach consists of an operator split technique, which transforms the elastic-plastic problem into a purely elastic problem and a residual problem with prescribed eigenstrains. The eigenstrains are determined using an incremental projection method. Contact stresses and contact residual stresses of meshing gear teeth with standard and modified profile are computed. The results show compressive residual stress can improve capacity of gear and operating life. This aspect may contribute to future developments in the understanding of gear durability.

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